The DHCP class has a public method for fetching the DHCP server IP address:
Unfortunately for you the Ethernet class keeps it's pointer to the DHCP object (_dhcp) private. If it didn't you could call:
IPAddress dhcpAddress = Ethernet._dhcp->getDhcpServerIp();
You can edit Ethernet.h to make that pointer public but your code would not be portable.
You could do your own DHCP request and pass the results to Ethernet.begin(). That would be the supported way. Just copy the code from EthernetClass::begin(uint8_t *mac_address) and when you have the DHCP results, call Ethernet.begin(uint8_t *mac, IPAddress local_ip, IPAddress dns_server, IPAddress gateway, IPAddress subnet).